A)
Multiple Choice
What is the value of n so that the expression x² + 11x + n is a perfect square trinomial?
(1 point)
11
25
30.25
36
36
A)
What is a solution of x² + 6x = –5?
(1 point)
x = –6
x = –1
x = 1
x = 6
B) x = -1
A)
Which of the following is a solution of x² + 14x + 112 = 0? If necessary, round to the nearest
hundredth.
(1 point)
x = –0.24
x = –4.24
4.24
no solution
B) x = -4.24
A)
A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in³ The
length is 4 inches greater than twice the width. What is the width of the box?
(1 point)
–10 in
8 in
20 in
40 in
The volume of a rectangular prism can be found using the formula V = length * width * height. Given that the volume is 2,720 in³ and the height is 17 in, we can substitute these values in along with the given relationship between the length and width provided in the problem.
Let's denote the width as W. Since the length is 4 inches greater than twice the width, the length can be expressed as 2W + 4.
Therefore, the volume equation becomes:
2W + 4 * W * 17 = 2,720
Solve for W:
34W + 68W = 2,720
102W = 2,720
W = 2,720 / 102
W = 26.67 (rounded to the nearest hundredth)
The width of the box is approximately 26.67 inches. However, none of the provided choices matches this answer exactly, therefore, the correct width should be 26.67 inches.
not a answer
Let's solve the problem considering the relationship between the dimensions of the rectangular prism as provided in the problem.
Let the width of the box be W inches.
The length is 4 inches greater than twice the width, so the length is 2W + 4 inches.
The height is given as 17 inches.
The volume of a rectangular prism is given by V = length * width * height
Given that the volume is 2,720 in³, we have:
(2W + 4) * W * 17 = 2,720
(34W + 68) * W = 2,720
34W² + 68W = 2,720
Dividing by 2:
17W² + 34W = 1,360
17W² + 34W - 1,360 = 0
We can solve this quadratic equation to find the possible values for W. By using the quadratic formula:
W = (-B ± √(B² - 4AC)) / 2A
W = (-34 ± √(34² - 4*17*-1,360)) / 2*17
W = (-34 ± √(1,156 + 9,280)) / 34
W = (-34 ± √10,436) / 34
W = (-34 ± 102.16) / 34
This gives two possible values for W:
W = (-34 + 102.16) / 34 = 68.16 / 34 = 2 (approximate)
W = (-34 - 102.16) / 34 = -136.16 / 34 = -4 (approximate)
Since the width cannot be negative in this context, the width of the box is approximately W = 2 inches.